Determinism and QM

[bascule]

As a firm believer in causal determinism, the (frustratingly inseperable) probabilistic nature of quantum always irked me. I had always relegated the Heisenberg Uncertainty Principle to a strictly observational problem and thought of the Schrodinger Equation as an observational abstraction which provided a model for generating probabilistic distributions to account for unobservable information.

 

I recently read a paper by Gerard 't Hooft of Utrecht University (http://www.phys.uu.nl/~thooft) entitled How Does God Play Dice? (Pre-)Determinism at the Planck Scale (PDF). There's also an accompanying presentation. He asserts an "information loss" hypothesis for non-determinism in QM which meshes quite well with my intuitive feeligs about the matter, but I'm afraid I don't fully comprehend his explanation, so I thought I'd link it here and see if anyone else was interested.

[Johnny5]

I don't fully comprehend his explanation either.

 

I don't think he does either, so that makes three of us.

 

I would start of questioning his first sentence

 

"Quantum mechanics works."

 

There are different interpretations of QM.

 

I think that's a source of confusion.

 

A question I would ask him though, is what is meant by 'determinism.'

[bascule]

A question I would ask him though, is what is meant by 'determinism.'

 

If we live in a discrete universe governed by causal determinism then then universe itself can "run" on a Universal Turing Machine and "now" would merely be the current iterative frame of some underlying state transition engine. I believe such a model of the universe is hypothesized in the form of loop quantum gravity

[Johnny5]

If we live in a discrete universe governed by causal determinism then then universe itself can "run" on a Universal Turing Machine and "now" would merely be the current iterative frame of some underlying state transition engine. I believe such a model of the universe is hypothesized in the form of loop quantum gravity

 

Hold your horses.

 

What is meant by "universe can run on a universal Turing machine"?

 

That's one question I have. I read about this awhile back, and figured out how I would approach the problem. (Godel sentence, and rules of how a UTM works. As I recall, the Universal Turing/truth machine, spits out true sentences when you ask it a question, but there is some kind of sentence which confuses the machine.)

 

The second question I have is this...

 

How do you connect the first question, together with the meaning of 'determinism" to loop quantum gravity?

 

So those are my two questions.

 

Regards

[aswokei]

A Turing machine? I've read a little about those from Stephen Wolfram. Turing machines are computer programs composed of a grid of separate and discrete cells that create results out of initial conditions and a particular set of rules. They are kind of like cellular automata.

 

http://www.turing.org.uk/turing/scrapbook/tmjava.html

 

As time goes on, evolution of such systems create results that are completely contingent on the states of the previous cells. Each cell's state is dependent on its immediate neighbors' states. This is probably why they are good models for natural systems. Ultimately, in all systems, everything is touching each other, touching, carrying messages. After a while of this evolution if the conditions are correct, complex and seemingly random structures can give way. What is meant, I believe by a universal Turing machine is a Turing machine that is able to emulate any other machine.

 

If everything in our universe is ultimately discrete (space, time, matter, energy), then it seems reasonable that such a system could be emulated by a program such as a Turing machine. Indeed, that's what Stephen Wolfram holds to be true. Our universe is a simple program, probably composed of only a few lines of code, running itself over into eternity. Pretty cool idea, I think.

[Johnny5]

A Turing machine? I've read a little about those from Stephen Wolfram. Turing machines are computer programs composed of a grid of separate and discrete cells that create results out of initial conditions and a particular set of rules. They are kind of like cellular automata.

 

http://www.turing.org.uk/turing/scrapbook/tmjava.html

 

That's not what I thought it was' date=' maybe I was thinking of something else.

 

Let me see if i can find what i was thinking of.

 

Here is what i was thinking of, i got universal turing machine confused with universal truth machine. When you said Godel that threw me off.

 

Godel's universal truth machine

 

There is an error in the reasoning Godel used.

 

 

At any rate that doesn't appear to be what you were talking about.

 

Also, if you have a link to what you read at Stephen Wolfram's site, I'd like to have a look at it. I went to the link you posted, and saw mention of three kinds of "Universal Turning Machines"

 

Regards

[reverse]

It’s funny how all roads lead to Rome.

 

While researching an entirely different topic, I was Quizzing “Alice” (an Artificial intelligence) on how she knew stuff.

 

She held the position that it was possible due to reductionism.

 

Which immediately bought about the concept of determinism in my mind.

Which immediately bought free will into question, - which immediately made me want to go have a cup of tea and breakfast.

( I’m easily distracted)

[reverse]

This looks like a good place to dive in at the deep end.

 

http://wa.lii.org/search?comment=018047

 

[bascule]

There is an error in the reasoning Godel used.

 

Yes! I have been saying this for years. Godel's proof works within the realm of math which in turn is constructed upon a set of underlying axioms. Thus Godel's incompleteness theorem only holds true for systems of mathematics which obey that underlying set of postulates.

 

Godel himself wrote extensively on the subject and his main argument seemed to be the insistance that because his proof holds true for our set of axioms then it still disproves it for whatever higher level system our mathematics is a subset of. He had a great deal of reasoning behind that assertion, but personally I think it's all bullshit.

[Johnny5]

Yes! I have been saying this for years. Godel's proof works within the realm of math which in turn is constructed upon a set of underlying axioms. Thus Godel's incompleteness theorem only holds true for systems of mathematics which obey that underlying set of postulates.

 

Godel himself wrote extensively on the subject and his main argument seemed to be the insistance that because his proof holds true for our set of axioms then it still disproves it for whatever higher level system our mathematics is a subset of. He had a great deal of reasoning behind that assertion' date=' but personally I think it's all bullshit.[/quote']

 

A set theoretic analysis of his work will reveal his error. He had several incompleteness theorems. Do you know of a way to isolate an error in either of them?

[AL]

A set theoretic analysis of his work will reveal his error. He had several incompleteness theorems. Do you know of a way to isolate an error in either of them?

Well this is certainly news to me. What exactly was Godel's error?

And I do hope you realize that set theory itself is incomplete? It wouldn't help your cause at all to use a "set theoretic analysis" to then refute Godel.

 

Godel himself wrote extensively on the subject and his main argument seemed to be the insistance that because his proof holds true for our set of axioms then it still disproves it for whatever higher level system our mathematics is a subset of. He had a great deal of reasoning behind that assertion, but personally I think it's all bullshit.

This objection seems self-refuting to me. If there is a "higher level system" or all-encompassing axiomatic system which covers all of mathematics, it would presumably allow for the construction of the natural numbers, or at least a concept of counting. If such were the case, Godel's theorem would apply to it.

[Johnny5]

Well this is certainly news to me. What exactly was Godel's error?

And I do hope you realize that set theory itself is incomplete? It wouldn't help your cause at all to use a "set theoretic analysis" to then refute Godel.

 

It is best to show what I mean symbolically, rather than debate set theory.

 

I only ran through his argument once, for a week or so, found a weak point, and haven't looked at it again.

 

I could just show you what I mean, and then you could critique it.

[reverse]

Guys, serious question for you.

 

do you realise what question you are asking?

 

do you see that you are asking if human reality is able to be represented by numbers?

 

will you confirm that for me so I know you know.

[Johnny5]

Guys' date=' serious question for you.

 

do you realise what question you are asking?

 

do you see that you are asking if human reality is able to be represented by numbers?

 

will you confirm that for me so I know you know.[/quote']

 

I don't think that anyone is claiming that reality is able to be represented by numbers. I'm not sure what that means.

 

This thread is about determinism, and quantum mechanics, and it has veered slightly to the issue of Godel's incompleteness theorem, and a possible connection to universal turing machines and determinism. Numbers are used to quantify things in the sciences. If you want to question whether or not that is valid in any particular scenario, then go right ahead. It is not pointless to wonder whether or not the distance between two points in space is accurately representence by the real number system.

 

You will find many physicists leaning nowadays to the natural number system, and quantization of variables... in quantum mechanics energy is quantized.

 

In fact, Ernst mach wrote something about this, let me see if i can find his quote, because it seems appropriate:

 

Ernst Mach wrote (p. 596 in ref. 1), "The view that makes mechanics the basis of the remaining branches of physics, and explains all physical phenomena by mechanical ideas, is in our judgment a prejudice. ... The mechanical theory of nature, is, undoubtedly, in a historical view, both intelligible and pardonable; and it may also, for a time, have been of much value. But, upon the whole, it is an artificial conception."

 

Classical mechanics is indeed inappropriate as a starting point for physics because it is not fundamental; rather, it is the limit of an incoherent aggregation of an enormous number of quantum elements. To make contact with the fundamental nature of matter, we must work in a coherent context where the quantum reality is preserved. source

 

As you can see, Mach had a leaning to the natural number system {1,2,3,4,...}.

 

Whether or not a given quantity of physics can be represented by natural numbers is a good question.

 

The concept of pi seconds does seem meaningless.

 

But then again, the concept of a quantum unit of time has difficulties which have yet to be overcome.

 

But scientists have to explain reality using numbers. They also use their natural language. But numbers are the basis of the "hard sciences."

 

Without numbers, scientists would never have been able to develop computers.

 

So even if you cannot model reality using numbers... you sure as hell can change it by using numbers.

 

Merely look at the existence of a computer, and you will see that's true.

 

Regards

[reverse]

Agree.

 

What was your interpretation of the word "determinism"?

[bascule]

do you realise what question you are asking?

 

do you see that you are asking if human reality is able to be represented by numbers?

 

Represented by numbers and the control logic for a Turing-complete state transition engine (which is inherently discrete and deterministic)

 

It's more akin to Conway's Life, which is a Turing-complete state transition engine. Everything in Life can be represented as binary sequences, but the sequences are essentially meaningless unless the state transition engine runs. I didn't mean to actually say that the universe "runs" on a Universal Turing Machine; what I really meant to say was that the underlying state transition engine is Turing-complete, i.e. you can use it to emulate a Universal Turing Machine. As an example here is Life being used to emulate a Universal Turing Machine:

 

http://rendell.server.org.uk/gol/turing_js_r.gif

 

This all fundamentally stems from my desire not to give up my common sense view of time as being either 'now' (the current state of the transition engine), 'past' (a state the transition engine has already been through), or 'future' (a state the transition engine must eventually be in due to the deterministic nature of its operation). It seems to me this has to hold true if reality is truly causally deterministic, i.e. all events in frame n of the state transition engine are causes of all events in frame n+1, which are effects of the causes in the previous frame. In a discrete causally deterministic universe there must be a minimum level of granularity in the flow of time, and therefore 'now' is very real.

 

If my understanding is correct, loop quantum gravity is both deterministic (i.e. non-probabilistic) and discrete.

[reverse]

This all fundamentally stems from my desire not to give up my common sense view of time as being either 'now' (the current state of the transition engine), 'past' (a state the transition engine has already been through), or 'future' .

 

This was my speculation as to why the A.I. “Alice” refuses to acknowledge the passage of time, even though it has a running time index .

[reverse]

Gents, what do you think of this in relation to the main topic?

 

http://www.generativeart.com/2000/MCGUIRE.HTM

[Johnny5]

Gents' date=' what do you think of this in relation to the main topic?

 

http://www.generativeart.com/2000/MCGUIRE.HTM[/quote']

 

I think its quite good. I don't know much about fractal geometry, although I do know that there's a link between it and chaos theory, and the concept of random.

 

It all goes to the meaning of the term 'deterministic.'

 

In my estimation, scientists do not yet have the concept of 'random' down.