Does the Observer have anything to do with conscious choice

[bhobba]

Which is a pure instrumentalist view with no room for any interpretations.

I have stated right from the outset this is the usual standard Copenhagen or Ensemble interpretation. If you want to go beyond that - fine - but please say that's what you are doing.

Why you think I have an issue with the relational view is beyond me. I have clearly stated I have always more or less assumed its like that anyway. My departure from it is it's not really of much value because once decoherence has occurred, which happens very very quickly, all observers agree.

Thanks
Bill

 

[bhobba]

I didn't realize that when a proton and an electron interacted as a hydrogen atom that they became entangled. Or two hydrogen atoms interacting become entangled.

It depends on the type of interaction - in that case they are - but not always.

Its not usually thought of that way though.

Thanks
Bill

 

[arkajad]

What a pure state is defined in the framework of generalized probabilistic theories of which bog standard probability theory and QM are just examples eg:
http://www.cgogolin.de/downloads/gpt.beamer.pdf
'Definition: States that can not be written as a convex combination of states are called pure or extremal.'

Let me recall Axiom 1 from Hardy's paper:

The state associated with a particular preparation is defined to be (that thing represented by) any
mathematical object that can be used to determine the probability associated with the outcomes of any measurement that may be performed on a system prepared by the given preparation.

Now, how do you take "convex combination" of "any mathematical object"?

It does not make sense. Evidently the author was not thinking deep enough at this point. So, how would you correct this axiom so that "convex combination" would make sense? Please, replace this axiom by some other so that what you are talking about would make sense.

 

[bhobba]

Now, how do you take "convex combination" of "any mathematical object"?
It does not make sense.

One more time then that's it for me - you obviously don't get it. And you will probably say I don't so there is really no point in continuing and going around in circles.

Of course you can't do it for any mathematical object. Generalized probabilistic theories are defined as theories you can. Such theories exist eg both standard probability theory and QM allow it but they are not the only ones - eg real vector space QM. That's all you need to know for the definition to not be vacuos.

Its used all the time in math - eg the abstract definition of a vector space you can add vectors - how do you add any mathematical object. The obvious answer is you can't - vector spaces are defined as ones you can. Generalized Probabilistic theories are defined as ones where convex sum makes sense. This implies the operation of addition and multiplication by a positive number makes sense.

Thanks
Bill

 

[arkajad]

Of course you can't do it for any mathematical object.

So, we have some progress. As it stands the axiom does not make sense. We agree on that.
So, how would you change so that it does make sense? Would you replace "any mathematical object" by, say "an element of a convex set in some vector space"?

 

[bhobba]

So, we have some progress. As it stands the axiom does not make sense.

It makes perfect sense. Axiom 5 applies to theories where convex sum makes sense like vector space applies to objects where sum makes sense.

Generalized probabilistic theories are defined as theories that contain objects called states such that convex sum makes sense ie if ui are states then Ʃ pi ui is also a state where Ʃ pi = 1 and pi positive. A state is pure if you can't find other states such it can be expressed as a convex sum of them.

We are just going around in circles and getting nowhere.

Thanks
Bill

 

[arkajad]

We are just going around in circles and getting nowhere.

We are going somewhere, though with unnecessary friction. Because that is (convex structure) what I was asking at the very beginning.

So, we are associating Particular preparations" with elements of some convex set (in a real vector space). We define pure states as extremal points of this set. That is ok mathematically. But we are discussing physics. "Preparations" is physics term. So my question is: are we able to distinguish between pure and mixed states experimentally? How? Does it make sense? Which "preparations" correspond to pure states and which to "nontrivially mixed states"? Can we do that analyzing preparation procedures? Or only through measurements? How many measurements are necessary? Can we do it in a finite set of measurements? Infinite? How? And when we talk about "state", do we mean "state of an individual system" or "state of an ensemble of identically prepared systems"?

 

[bhobba]

That is ok mathematically. But we are discussing physics.

We are discussing mathematical models. Probabilistic models can be applied to physics, finance, economics and probably tons of other stuff I can't think of off the top of my head. Generalized probability models have certain well defined mathematical properties such as states that have a defined convex sum.

I was not trained in physics, but in applied math and mathematical modelling uses this sort of thing all the time.

The answer to your questions is contained in the model. The assumption of a mathematical model is it makes sense. Are you denying that probability models do not exist that makes sense? Do you deny that bog standard probability theory, which is a probabilistic model makes sense? Many of those questions you are asking are the general crap you hear about when discussing say the frequency interpretation of probability. To be blunt I have been through that one before and, again to be blunt, its philosophical waffle of highly dubious value. What did my statistical modelling professor say about it - it's like discussing Nietzsche - rather pointless really. That got a big laugh in the class - but you know what - he was right.

But like I say - I am an applied mathematician, you have been trained in philosophy, we are worlds apart in approach I suspect.

Thanks
Bill

 

[arkajad]

I was not trained in physics, but in applied math and mathematical modelling uses this sort of thing all the time.

Thanks a lot. And I apologize.

 

[meBigGuy]

Why you think I have an issue with the relational view is beyond me. I have clearly stated I have always more or less assumed its like that anyway. My departure from it is it's not really of much value because once decoherence has occurred, which happens very very quickly, all observers agree.

I don't see how that fits Wikipedia's description of relational QM Interpretation. I quoted two sentences, twice now, that had no inking of rapid decoherence. I'm saying that unobserved (by me) unentangled particles can interact. That one party sees a superposition, another sees a collapsed state. You say that difference is fleeting. I think Relational Interpretations say otherwise. Am I totally wrong?

From the Wikipedia page on RQM
"RQM argues that the notion of "state" describes not the observed system itself, but the relationship, or correlation, between the system and its observer(s). " <snip>
"Any "measurement event" is seen simply as an ordinary physical interaction, an establishment of the sort of correlation discussed above."

This seems totally different from other interpretations.

 

[meBigGuy]

From Wikipedia:
RQM is, in essence, quite similar to the Copenhagen interpretation, but with an important difference. In the Copenhagen interpretation, the macroscopic world is assumed to be intrinsically classical in nature, and wave function collapse occurs when a quantum system interacts with macroscopic apparatus. In RQM, any interaction, be it micro or macroscopic, causes the linearity of Schrödinger evolution to break down. RQM could recover a Copenhagen-like view of the world by assigning a privileged status (not dissimilar to a preferred frame in relativity) to the classical world. However, by doing this one would lose sight of the key features that RQM brings to our view of the quantum world.

 

[bhobba]

I don't see how that fits Wikipedia's description of relational QM Interpretation. I quoted two sentences, twice now, that had no inking of rapid decoherence

That's the exact problem with it - it hasn't taken on the lessons of decoherence.

Once you do that you see its really to required - not wrong - simply not required.

Thanks
Bill

 

[meBigGuy]

Now, that's finally a real point. I'll watch Susskind and get back to you.