Measurement Problem 2

Here are Stephen's cogent remarks reprinted
Marvin's reponse follows it:

The point you make, namely, that you "cannot believe that an intricate mathematical subtlety can be at the bottom of the conundrum that something about the nature of making a measurement demands a re-zeroing of the state of the universe" is one I take issue with.

On the contrary, I believe that it is exactly as an "intricate mathematical subtlety" that ANYTHING involving the nexus between our classical minds and the quantum regime is likely to appear to us macroscopic beings. That is, in a form counter to our intuitions, which is what I take to be your meaning of the words "intricate" and "subtle".

We do not have the internal epistemology to apprehend the quantum world as it actually is. We would not have evolved if we had had it. All classical reductions like hidden variables theories, etc., have been disposed of. We are left with no classical fall-back positions to explain anything, so why should this punctus crucis of classical-quantum interchange appear simple to us in any way? Particularly as the classical "world" does not exist. It is a fiction of our particular evolutionary tree. All is quantum, as David Finkelstein was fond of saying. What words would you use to simply describe something like this? It would have to be entirely within the vocabulary of QM: and then you are back with Hilbert space and its intricacies, which are real. This is not a proof that it cannot be done, but it is strong evidence to my mind.

For further evidence, I would direct you to two of the best theorems in the subject: the Kochen-Specker No Go Theorem, and Gleason's Theorem on the representability of states in terms of density matrices in Hilbert spaces of dimension greater than 2. A lot of the best things we know about QM are based on these results, which are intricate in the extreme.

Suppose the proofs of whatever for instance Bub has done could be much simplified. Would you be happier? Or must it be an entirely non-mathematical explanation?

My own view is one of extreme operationalism adopted from Finkelstein. There are no objects in the actual world, only possible experiments. Therefore no "objective" observers. No observers, actually, only primitives called "experiments". Quantum theory is a language for describing possible experiments.

Response to Stephen's cogent remarks

I loved reading what you wrote. So very stimulating. I'm not sure that we disagree all that much. We both appreciate the fundamental notion that 'understanding' consists in discovering the mathematics that describes reality. But having discovered it we can ask what does it tell us about how to perceive reality. What's the story?

The process of discovery involves mind structures, ways of thinking, and especially postulates about reality. The "intricate mathematical subtlety" must have some narrative attached to it.



I offer a measurement problem animation to illustrate a narrative. Press the particle release button to have a vertically polarized particle traverse the field gradient region. Made visible here by icons is what is not measurable: the particle amplitude. The act of detection means that the particle gets merged into a large dimensioned hilbert space. How does this fact demand that one of the choices materialize? And if it is all causal, how is one or the other choice chosen? What is the substance of the matter? I find it hard to consider something explained simply by 'that's the way it works out'.

I need a satisfying picture, an acceptable narrative. A metaphore for the mathematics. It is not enough for me to be told, "Here look at the mathematical result." That's what generates intuition on the matter, a narrative.

Rovelli seems to have a narrative. But it is not clear to me how the measurement problem is resolved by the relativity of measurement.

Perhaps Stephen will give the substance of what the "Kochen-Specker No Go Theorem and Gleason's Theorem" tell us. I'd certainly appreciate understanding the significance of these two results.

Splittings of the Universe

Somehow the answer to these questions must be explicable in terms other than it "comes out of a subtle result on the structure of Hilbert spaces".

Stephen says:
It would be nice, but I'm not sure that it "must be" explicable so easily. We really lack the intuitions and therefore the vocabulary here in the macrocosm. I think it would be important to be able to do it simply, but no-one has managed it to my knowledge.

@Stephen
I cannot believe that an intricate mathematical subtletly can be at the bottom of the conundrum that something about the nature of making a measurement demands a sudden re-zeroing of the state of the universe. On measurement one deterministic process suddenly ceases and a new one begins! The answer must, indeed, have a mathematical embodiment but we ask what specific character of the structure of hilbert space connects with these interminable splittings of the universe at each measurement event.

Measurement Problem

Rovelli's work is 2006. see http://arxiv.org/abs/quant-ph/9609002. When I think about it I don't see how he solves the measurement problem. He solves Schroedinger's cat. Idea: The cat measures the radioactive decay by dieing or not. But you can't talk about the cat until you interact with it by opening the box. I like Rovelli's notion that there is no distinction between observer and the observed. Everything is a system: observer or observed are just interacting systems. But the measurement problem is far more profound. I gathered some quotes to state it.

ALL POSSIBILITIES ARE LEFT OPEN. BUT A DEFINITE OUTCOME OCCURS.

“The quantum measurement parodox.. stated succinctly... In quantum mechanics all possibilities... are left open whereas in ... experience a definite outcome always (occurs).”
A. J. Leggett in
Foundation of Physics. 18, 939 (1988)

“How is the measuring instrument proded into making up its mind which value it has observed?”
Bryce S. Dewitt Physics Today 23, 30 (1970)

“Some explanation must be provided for the fact that the Hilbert—space vector... collapses onto a certain eigenvector during a measurement process...”
J. Bub, Nuovo Cimento v. 57, Nr.2, 503 (1968)

The probability amplitudes evolve deterministically until a measurement is made: the measurement stops the evolution. What is the essential element that changes the evolution of the system from being in a state |S> = superposition of states |n>, into being in a state |n=3>, one from among the superposition? Marvin Chester, never published

Somehow the answer to these questions must be explicable in terms other than it "comes out of a subtle result on the structure of Hilbert spaces".

Ant's World View

The interesting thing about suicide bombers is this: that they are so dedicated to their community - islam, anarchism in a former time - that they kill themselves for it.

Let us distinguish the practice from the mechanisms by which they are persuaded. The mechanism requires a world view - a belief in the supernatural, in an afterlife, in unseen powers around us which we must placate, a belief in a greater good.

What persuades the ants to kill themselves for their community? Do ants have a world view?

"Is Life Worth Living?" asks William James

In Is Life Worth Living? by William James James says: "Pessimism is essentially a religious disease."

He clarifies thusly: This "is why I call pessimism an essentially religious disease The nightmare view of life [arises from] the contradiction between the phenomena of Nature and the craving of the heart to believe that behind Nature there is a spirit whose expression Nature is."

He is wrong. Pessimism is a purely chemical phenomenon. Proof: Smoke a little marijuana and life becomes worth living.

Economics Animated

I was very impressed by http://www.youtube.com/v/SA1f2MefsMM

This is as fine an expostion on economics as I have ever seen. Unfortunately the enthusuastic narrator speeds up his speech exactly where he should be slowest - in the more complicated later sections. This leaves me with the impression, unfortunately, that some hype is involved in his exposition. References for his assertions are lacking. Too much righteous indignation comes through. He resents that the rich are getting richer and the poor are getting poorer. That this is, indeed, the case is his thesis and he certainly seems to prove it masterfully - clearly, intelligently and completely.

What is truly wonderful about the presentation is its clarity. Arnold's symbolic representations of ideas is the work of a master intellect. He makes a great contribution to thought exposition.

The video is part of a series which can be accessed at
http://www.youtube.com/user/leearnold

Below is the first of this remarkable Lee Arnold series and his Ecolanguage invention.

.swf embed

The code below is what inserted the .swf file.

<embed src = "http://chesters.org/marvin/RandomWalk/walkDsplay.swf" quality="high" bgcolor="#c0c0c0" width="360" height="360" align="middle" allowScriptAccess = "sameDomain" type = "application/x-shockwave-flash" pluginspage = "http://www.macromedia.com/go/getflashplayer"/> </embed>

just checking

OK This is my first blog post. Just testing. Let's see what happens. Wondering whether can post mathematical equations, flash animation...
I'm going to check the link button
http://chesters.org
I see that there is an EditHtml choice. I wonder whether I could post a flash item there. At any rate here is an elfi drawing.