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Author Topic:   Chance moves in mysterious ways.
sinequanon
Member (Idle past 1035 days)
Posts: 331
Joined: 12-17-2007


Message 91 of 99 (443646)
12-26-2007 8:47 AM
Reply to: Message 90 by Son Goku
12-26-2007 8:09 AM


Re: Quantum Mechanics.
Well for instance if QM had any other norm higher than the square norm it would be physically trivial.

That's not unique to QM. Any second order linear partial system has the same operation. Think of energy considerations.

What do you mean by a "higher" norm? And what evidence do you have that other norms are physically trivial?

Unless I’m very mistaken about QM, all this is specifically the structure of the non-deterministic component. The deterministic component is a Schrödinger-type equation.

That sounds confused.

The linear operations on the space are derived using the Schrodinger equation.

I don’t understand this. How does the fact that other systems have structure say anything about QM’s indeterminate aspects?

It doesn't. It says, apart from QM, there are other structurally rich systems that can be modelled in complex space.

It therefore lends support to asserting that there is randomness.

I have not said randomness doesn't exist. However, PaulK's abortive logic may have led to that conclusion somewhere.


This message is a reply to:
 Message 90 by Son Goku, posted 12-26-2007 8:09 AM Son Goku has responded

Replies to this message:
 Message 92 by Son Goku, posted 12-26-2007 11:09 AM sinequanon has responded

  
Son Goku
Member
Posts: 1121
From: Ireland
Joined: 07-16-2005


Message 92 of 99 (443664)
12-26-2007 11:09 AM
Reply to: Message 91 by sinequanon
12-26-2007 8:47 AM


Re: Quantum Mechanics.
sinequanon writes:

That's not unique to QM. Any second order linear partial system has the same operation. Think of energy considerations.


Huh? What theory besides QM uses a 2-norm? How does it relate to energy?

sinequanon writes:

That sounds confused.

The linear operations on the space are derived using the Schrodinger equation.


They are? How so? That certainly isn't what happened historically. The Schrodinger equation alone only gives unitary evolution. If you only had that, you'd think you were dealing with a standard physical PDE describing wave evolution. It's Born's 2-norm probability that then gives meanings to linear operators and their eigenvalues.

sinequanon writes:

What do you mean by a "higher" norm? And what evidence do you have that other norms are physically trivial?


It would make the post too turgid to go into. Any questions have their answer here:
http://www.scottaaronson.com/papers/island.pdf

sinequanon writes:

It says, apart from QM, there are other structurally rich systems that can be modelled in complex space.


Yes, I understand that. Other things use complex numbers, why does it matter though? What are you saying?

sinequanon writes:

I have not said randomness doesn't exist.


Fair enough. However if randomness has experimental tests such as the Aspect experiments which can directly falsify it then part of your original claim isn't true.
sinequanon writes:

I believe the existence of randomness is neither verified nor falsifiable. Furthermore, I do not believe it is verifiable.


The reason I'm bringing up this point about the mathematical structure in QM is because I'm trying to demonstrate that the random component has:
(a) Experimental support and the existence of experiments capable of falsifying it.
(b) We have found out properties of this randomness. Such as it having the 2-norm I describe above. This is a major insight. The existence of statistics other than the 1-norm humans had used up to then.

This indicates that randomness is a feature of the world with properties scientists can study. This is a world away from

sinequanon writes:

"Randomness done it" is as rigorous as "God done it".


This message is a reply to:
 Message 91 by sinequanon, posted 12-26-2007 8:47 AM sinequanon has responded

Replies to this message:
 Message 93 by sinequanon, posted 12-26-2007 12:01 PM Son Goku has responded

  
sinequanon
Member (Idle past 1035 days)
Posts: 331
Joined: 12-17-2007


Message 93 of 99 (443678)
12-26-2007 12:01 PM
Reply to: Message 92 by Son Goku
12-26-2007 11:09 AM


Re: Quantum Mechanics.
Huh? What theory besides QM uses a 2-norm? How does it relate to energy?

The length of a vector is a "2-norm". I'll leave the rest to you.

It's Born's 2-norm probability that then gives meanings to linear operators and their eigenvalues.

The linear self adjoint Hamiltonian operator is derived from the time independent Schrodinger equation. That is where the eigenfunctions come from.

It would make the post too turgid to go into. Any questions have their answer here:

He's basically saying, in very flowery language, that length is preserved under rotation. That's not special to the QM model.

Yes, I understand that. Other things use complex numbers, why does it matter though? What are you saying?

Ignore. It's an answer to an earlier question of yours, not a new point.

I think it is getting circular. I believe you have mentioned a few mathematical terms without really understanding the mathematical detail. As we have each stated our perspective and are unlikely to reconcile them, I think we should leave interpretation to the insight of the reader.


This message is a reply to:
 Message 92 by Son Goku, posted 12-26-2007 11:09 AM Son Goku has responded

Replies to this message:
 Message 94 by cavediver, posted 12-26-2007 12:11 PM sinequanon has responded
 Message 95 by Son Goku, posted 12-26-2007 12:20 PM sinequanon has not yet responded
 Message 96 by Chiroptera, posted 12-26-2007 12:23 PM sinequanon has not yet responded

  
cavediver
Member (Idle past 1814 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 94 of 99 (443680)
12-26-2007 12:11 PM
Reply to: Message 93 by sinequanon
12-26-2007 12:01 PM


Re: Quantum Mechanics.
Huh? What theory besides QM uses a 2-norm? How does it relate to energy?

The length of a vector is a "2-norm". I'll leave the rest to you.

It's Born's 2-norm probability that then gives meanings to linear operators and their eigenvalues.

The linear self adjoint Hamiltonian operator is derived from the time independent Schrodinger equation. That is where the eigenfunctions come from.

It would make the post too turgid to go into. Any questions have their answer here:

He's basically saying, in very flowery language, that length is preserved under rotation. That's not special to the QM model...

...I think it is getting circular. I believe you have mentioned a few mathematical terms without really understanding the mathematical detail. As we have each stated our perspective and are unlikely to reconcile them, I think we should leave interpretation to the insight of the reader.

:laugh: Yes, and this reader has quickly come to the conclusion that you really know very little about QM, although perhaps a tad more than your cosmology. There are some gems above that will leave SG speachless :D

Anyway, just a couple of points for both of you. It is quite possible that determinism will be restored in a deeper theory to QM, and this has been worked on for some time, both with decoherence and more recent work. Don't forget that all the Apsect experiments demonstrate is that there are no hidden CLASSICAL variables. It is all about statistics, and statistics do not in themselevs imply indeterminism.


This message is a reply to:
 Message 93 by sinequanon, posted 12-26-2007 12:01 PM sinequanon has responded

Replies to this message:
 Message 98 by Son Goku, posted 12-26-2007 12:29 PM cavediver has not yet responded
 Message 99 by sinequanon, posted 12-27-2007 7:09 AM cavediver has not yet responded

  
Son Goku
Member
Posts: 1121
From: Ireland
Joined: 07-16-2005


Message 95 of 99 (443686)
12-26-2007 12:20 PM
Reply to: Message 93 by sinequanon
12-26-2007 12:01 PM


Re: Quantum Mechanics.
sinequanon writes:

I think it is getting circular. I believe you have mentioned a few mathematical terms without really understanding the mathematical detail. As we have each stated our perspective and are unlikely to reconcile them, I think we should leave interpretation to the insight of the reader.


What about the last part of my post about the existence of a falsification test for randomness, which you claim does not exist? The fact that it does exist is a direct refutation of your position.

sinequanon writes:

The length of a vector is a "2-norm". I'll leave the rest to you.


Obviously there exist cases where one gets the length of things with a binary operation. The point is, the fact that QM uses 2-norm probability is something new and interesting. It was never seen before in standard statistics and gives rise to new physical effects. This is an important point, because you calim that "randomness did it" is as good as "God did it", which obviously can't be the case unless "God did it" somehow implies which normed statistics you should use.

Eigenfunctions of energy. That's one single operator. And it doesn't even mean anything until you have the square modulus (2-norm) Born rule. Sure why weren't Hilbert Spaces used before in physics?

He's basically saying, in very flowery language, that length is preserved under rotation. That's not special to the QM model.

You cannot be serious. That's like saying "All relativity says is that different things see different stuff, big deal".
This message is a reply to:
 Message 93 by sinequanon, posted 12-26-2007 12:01 PM sinequanon has not yet responded

  
Chiroptera
Member
Posts: 6639
From: Oklahoma
Joined: 09-28-2003
Member Rating: 4.9


Message 96 of 99 (443687)
12-26-2007 12:23 PM
Reply to: Message 93 by sinequanon
12-26-2007 12:01 PM


Re: Quantum Mechanics.
I believe you have mentioned a few mathematical terms without really understanding the mathematical detail.

Okay, this makes me feel better. I will take it as a possibility when you say this to me, but when you are now saying this to Son Goku I know you're a nut.


"The guilty one is not he who commits the sin, but the one who causes the darkness."
Clearly, he had his own strange way of judging things. I suspect that he acquired it from the Gospels. -- Victor Hugo
This message is a reply to:
 Message 93 by sinequanon, posted 12-26-2007 12:01 PM sinequanon has not yet responded

  
Chiroptera
Member
Posts: 6639
From: Oklahoma
Joined: 09-28-2003
Member Rating: 4.9


Message 97 of 99 (443689)
12-26-2007 12:27 PM
Reply to: Message 87 by sinequanon
12-24-2007 7:44 AM


I'm reminded of a certain scene between Jamie Lee Curtis and Kevin Kline....
I haven't read that particular book, but I have covered the standard mathematics university courses on QM and using Hilbert spaces and the Hermitian operator. We went up to the basics of string theory.

Um, how much of it did you actually understand?


"The guilty one is not he who commits the sin, but the one who causes the darkness."
Clearly, he had his own strange way of judging things. I suspect that he acquired it from the Gospels. -- Victor Hugo
This message is a reply to:
 Message 87 by sinequanon, posted 12-24-2007 7:44 AM sinequanon has not yet responded

  
Son Goku
Member
Posts: 1121
From: Ireland
Joined: 07-16-2005


Message 98 of 99 (443690)
12-26-2007 12:29 PM
Reply to: Message 94 by cavediver
12-26-2007 12:11 PM


Re: Quantum Mechanics.
cavediver writes:

Anyway, just a couple of points for both of you. It is quite possible that determinism will be restored in a deeper theory to QM, and this has been worked on for some time, both with decoherence and more recent work. Don't forget that all the Apsect experiments demonstrate is that there are no hidden CLASSICAL variables. It is all about statistics, and statistics do not in themselevs imply indeterminism.


Yes, to be fair work on this stuff does exist. There could be a deeper deterministic theory underneath QM*. I'm trying to show that QM's randomness isn't scientifically worthless.

Think of it as being like somebody defending Newton's action-at-distance theories two hundred years ago. Some people might claim that the action happening at a distance is like saying "God magically did it instantly". You'd defend it by describing everything it has done, perhaps unfairly ignoring the work of "propagation" theorists who could turn out to have the right answer.

*As a side note do you know of a deterministic model which can replicate QFT. Every deterministic model I've ever seen only matches QM's predictions not QFTs. For example Bohmian Mechanics.


This message is a reply to:
 Message 94 by cavediver, posted 12-26-2007 12:11 PM cavediver has not yet responded

  
sinequanon
Member (Idle past 1035 days)
Posts: 331
Joined: 12-17-2007


Message 99 of 99 (443864)
12-27-2007 7:09 AM
Reply to: Message 94 by cavediver
12-26-2007 12:11 PM


Re: Quantum Mechanics.
Anyway, just a couple of points for both of you. It is quite possible that determinism will be restored in a deeper theory to QM, and this has been worked on for some time, both with decoherence and more recent work. Don't forget that all the Apsect experiments demonstrate is that there are no hidden CLASSICAL variables. It is all about statistics, and statistics do not in themselevs imply indeterminism.

What would this "quite possible" restoration of determinism mean for the uncertainty principle? I take it that it could NO LONGER be a principle.


This message is a reply to:
 Message 94 by cavediver, posted 12-26-2007 12:11 PM cavediver has not yet responded

  
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